Eigenfunctions decay for magnetic pseudodifferential operators

Details Eigenfunctions decay for magnetic pseudodifferential operators Eigenfunctions decay for magnetic pseudodifferential operators

2010-05-11

arxiv.org/abs/1005.1743v1

Mathematics

Analysis of PDEs

Scientific paper

We prove rapid decay (even exponential decay under some stronger assumptions)
of the eigenfunctions associated to discrete eigenvalues, for a class of
self-adjoint operators in $L^2(\mathbb{R}^d)$ defined by ``magnetic''
pseudodifferential operators (studied in \cite{IMP1}). This class contains the
relativistic Schr\"{o}dinger operator with magnetic field.

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